Nano‐imaging through tip‐enhanced Raman spectroscopy: Stepping beyond the classical limits

The spatial resolution in optical imaging is restricted by so‐called diffraction limit, which prevents it to be better than about half of the wavelength of the probing light. Tip‐enhanced Raman spectroscopy (TERS), which is based on the SPP‐induced plasmonic enhancement and confinement of light near a metallic nanostructure, can however, overcome this barrier and produce optical images far beyond the diffraction limit. Here in this article, the basic phenomenon involved in TERS is reviewed, and the high spatial resolution achieved in optical imaging through this technique is discussed. Further, it is shown that when TERS is combined with some other physical phenomena, the spatial resolution can be dramatically improved. Particularly, by including tip‐applied extremely localized pressure in TERS process, it has been demonstrated that a spatial resolution as high as 4 nm could be achieved.     

Real-time quantification of viable bacteria in liquid medium using infrared thermography

Quantifying viable bacteria in liquids is important in environmental, food processing, manufacturing, and medical applications. Since vegetative bacteria generate heat as a result of biochemical reactions associated with cellular functions, thermal sensing techniques, including infrared thermography (IRT), have been used to detect viable cells in biologic samples. We developed a novel method that extends the dynamic range and improves the sensitivity of bacterial quantification by IRT. The approach uses IRT video, thermodynamics laws, and heat transfer mechanisms to directly measure, in real-time, the amount of energy lost as heat from the surface of a liquid sample containing bacteria when the specimen cools to a lower temperature over 2 min. We show that the Energy Content (EC) of liquid media containing as few as 120 colony-forming units (CFU) of Escherichia coli per ml was significantly higher than that of sterile media (P < 0.0001), and that EC and viable counts were strongly positively correlated (r = 0.986) over a range of 120 to approximately 5 × 10⁸ CFU/ml. Our IRT approach is a unique non-contact method that provides real-time bacterial enumeration over a wide dynamic range without the need for sample concentration, modification, or destruction. The approach could be adapted to quantify other living cells in a liquid milieu and has the potential for automation and high throughput.     

An improved technique for holographic recording on a thermoplastic photoconductor

A new method for holographic recording on a thermoplastic-photoconductor has been developed. By using this new method which involves the application of white light to the thermoplastic-photoconductor after exposure, the sensitivity, reciprocity and signal-to-noise ratio have been improved. A higher diffraction efficiency (about 30%) can also be obtained.     

Temperature stabilized optical waveguide modulator

A low drive-voltage optical modulator using a Ti-diffused UNbO₃ optical waveguide has been fabricated. Stabilization against ambient temperature change was realized by using a miniature halfwave plate. The halfwave voltage, 3 dB bandwidth, optical insertion loss and extinction ratio were 3·8 V (at 1·06m wavelength), 850 MHz, 10 dB and 13 dB, respectively. A reduction scheme for the optical absorption caused by metallic electrodes, and an analysis of the modulator high frequency response are also reported.     

A study of Feynman integrals by micro-differential equations

We use the holonomic character of Feynman integrals to describe their singularity structure explicitly in some simple cases. The results in §1 show that under moderate conditions Feynman amplitudes can be locally expressed essentially in terms of Legendre functions near the points where two positive- Landau-Nakanishi surfaces meet. Related topics such as hierarchical principle in perturbation theory are also discussed in terms of holonomic systems involved. In §4 we use the concrete expressions for Feynman amplitudes obtained in §1 to discuss the validity of Sato's conjecture.Supported in part by NSF MCS 75-2333Supported in part by NSF GP 36269     

Ultrasonic study on the elastic moduli of the NaTl (B32) structure

The elastic moduli and Debye temperatures of LiAl, LiIn, LiZn, NaIn and NaTl (NaTl type: space group Fd3m) have been determined at room temperature by an ultrasonic pulse transmission technique. The trend between the isotropic bulk modulus (B) and the volume per atom pair ($\text{M}\text{ρ}$) shows that the simple coulombic form of ion-ion interaction is not applicable to the NaTl type structure, while the semiconductor like diamond- or ZnS-, and ionic CsCl-type crystals have contributions from a coulombic attractive force. The bonding character of the NaTl structure is also discussed.     

Uniform convexity of ψ-direct sums of Banach spaces

Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕_ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕_ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?_p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?_p,q is the Lorentz sequence space. These results extend the well-known fact for the ?_p-sum . Some other examples are also presented.